Rethreaded tires often become defective because the vulcanized rethread band becomes detached due mainly to heating during use of the tire. This is especially noticeable in rethreaded tires used for trucks and the like heavy road vehicles. The practice has recently developed to make transverse slits spaced along the entire length of the rethread band in order to prevent overheating of the tire during use. These slits cannot be made during the moulding and vulcanizing of the rethread band. Up to now, it was usual to use a rotating circular blade to make those slits. However, such rotating blades, when cutting across rubber or similar elastomeric material heat up very quickly and become clogged with elastomeric material adhering thereto.